Asymptotic of Approximate Least Squares Estimators of Parameters Two-Dimensional Chirp Signal

TL;DR

This paper develops asymptotic theory for approximate least squares estimators in 2-D chirp models, offering a computationally efficient alternative to traditional LSEs with proven asymptotic properties.

Contribution

It introduces an ALSE for 2-D chirp parameters, extending periodogram methods and providing a sequential estimation approach for multiple components.

Findings

ALSEs are asymptotically equivalent to LSEs.

The proposed method reduces computational complexity.

Simulation studies validate the effectiveness of the approach.

Abstract

In this paper, we address the problem of parameter estimation of a 2-D chirp model under the assumption that the errors are stationary. We extend the 2-D periodogram method for the sinusoidal model, to find initial values to use in any iterative procedure to compute the least squares estimators (LSEs) of the unknown parameters, to the 2-D chirp model. Next we propose an estimator, known as the approximate least squares estimator (ALSE), that is obtained by maximising a periodogram-type function and is observed to be asymptotically equivalent to the LSE. Moreover the asymptotic properties of these estimators are obtained under slightly mild conditions than those required for the LSEs. For the multiple component 2-D chirp model, we propose a sequential method of estimation of the ALSEs, that significantly reduces the computational difficulty involved in reckoning the LSEs and the ALSEs. We perform some simulation studies to see how the proposed method works and a data set has been analysed for illustrative purposes.